clvi Tables for Statisticians and Biometricians [XXXII XXXIV 



Further, <fc (pr) = i (rp + 2), </> 2 ( / )r) = T ^(3rp + 2) 2 , 

 </* (^) = TT ft ra {15 (rp) 3 + 18 (rp) 2 - 4 (rp) - 8}, 

 4>4 (pr) = jjttre {175 (rp) 4 + 200 (rp) 3 - 120 (rp) 2 - 160 (rp) - 16}. 



?i-2 

 In Table XXXIII the values of log / , of log (1 - p 2 )*, of log XL, log xz and 



of </>i, $2> $3 and </>4 are tabled for values of r proceeding by '05 and of p by '1. It 

 is accordingly possible to find with relative ease for the range of n mentioned 

 above the value of any ordinate. 



It will be noted that all the functions dealt with are symmetrical in r and p 

 except log (1 p 2 )^. Thus we have the result 



y (n, r, p) = y (n, p, r) 

 (1-p 2 )* (l-r 2 )*' 

 or, the ordinate at p for samples of n drawn from an indefinitely large normal 



/I_ r 2x| 



population of correlation r is equal to f ^ -- 2 j times the ordinate at r for samples 

 of the same size drawn from a like population of correlation p. 



Illustration (i). For n= 13, the ordinate at r = '9 for p = '7 is 1203*06. Therefore 

 the ordinate at r = '7 for p = '9 should be 



= 1203-06 (if)* = 1203-06 (jf Mf T )} 



= 1203-06 x (-05170711114)* = 1203-06 x -227,392 = 273-566. 

 The value tabled is 273'57. 



Illustration (ii). Find the value for a sample of 10 of the ordinate at r = '55 

 when p = '7. 



We take out of Table XXXIII, p. 217, 



log (l-p2)f = 1-561,3553, 

 log Xl = -013,3179, log X z = T'831,3240, 



77 2 



and from p. 2 12, log -^= = = -425,9687. 



vn 1 



Hence for the preliminary part Y n of y (n, r, p), 



n 2 



log Y n = log -==- + log (1 - p 2 )* - 9 log xi - log % 2 , 

 vn- 1 



we have 1-561,3553 -_-119,8611 



425,9687 1-831,3240 

 1-987,3240 -1-951,1 851 



= -036,1389, 

 or Y n = 1-086,7 73. 



